## What Is Resonance?

We hear the word used a lot, but what is resonance? First, in order to explain we have to explain the terms we will use.

• A period is the amount of time it takes to complete one cycle
• The number of cycles in one second is the frequency of an oscillation.
• Frequency is measured in Hertz, named after the 19th-century German physicist Heinrich Rudolf Hertz
• One Hertz is equal to one cycle per second.

### What Is Resonance?

A resonance occurs when a structure or material naturally oscillates at a high amplitude at a specific frequency. This frequency is known as a structural resonant frequency. Typically a structure will have many resonant frequencies.

A dictionary definition of resonance gives us –

“the state of a system in which an abnormally large vibration is produced in response to an external stimulus, occurring when the frequency of the stimulus is the same, or nearly the same, as the natural vibration frequency of the system.”

When the damping in a structure is small, the resonant frequencies are approximately equal to the natural frequencies of the structure, which are the frequencies of free vibrations of the molecules of the material itself.

Furthermore, an individual resonance is the condition when a natural frequency of a structure or material and the frequency at which it is being excited are equal or very nearly equal. This results in the structure or material vibrating strongly and is the classical resonance state. This resonance state can often lead to unexpected behaviour of the structure or material.

The lowest natural frequency, often called the fundamental frequency, is related to the material of which the structure is made. The greater the mass or density of the material the lower the fundamental frequency of vibration. The natural frequency is also related to the speed that a waveform can propagate through the structure. This is determined largely by the molecular make up of the material. Gas, for example, has many free molecules with high kinetic energy, so the waveform can move quickly through the material. A solid has far fewer free molecules and is much denser, therefore the waveform moves more slowly.

In order to measure a resonance of a structure or material with a Prosig P8000 data acquisition system and DATS Professional signal processing software it is necessary to attach an accelerometer to the structure. It is then required to excite or stimulate the structure with the frequencies that it is normally exposed to in its working life. For example, an automotive car tyre would need to be subject to the frequencies it would encounter whilst in use. This would normally be accomplished by use of a shaker or a large heavy hammer. The tyre for example would need to be tested in isolation, and not connected to anything else like the vehicle suspension or wheel rim as these other parts have their own resonant frequencies and would make the capture and analysis of the tyre resonant frequency difficult.

The measured response from the accelerometer will be relative to the excitation and will only exhibit frequencies that are present in the excitation. The excitation must be an acceptable representation of the normal working frequencies applied to the structure or material. If the structure has a resonance in this frequency range there will be a large peak in the response spectrum. The frequency of this peak will correspond to one of the resonant frequencies of the structure or material. If no peak is detected then the resonant frequencies lie outside the operating range of the structure or material. In order to find the resonant frequencies of a structure or material it may be necessary to apply a wider range of frequency excitation.

Figure 1 shows a frequency spectrum, this spectrum is a response of a structure to its excitation. A large spike can clearly be seen at approximately 250 Hz.

Figure 2 shows a frequency spectrum, this spectrum as in Figure 1 shows a frequency response. However, Figure 2 shows, using cursors, the exact frequency of the resonance. In this case the resonant frequency is 245 Hz.

This means that this structure should probably not be used if in its working life it will be exposed to this frequency. Figure 2 also shows that if this structure was to be used, and only exposed to 300Hz to 400 Hz or perhaps 0Hz to 200Hz , this particular resonant frequency would not be excited, and therefore the structure would not vibrate abnormally.

What Is Resonance? (part 2) (https://blog.prosig.com/2012/08/20/what-is-resonance-part-2/)
What Is Resonance? (part 3) (https://blog.prosig.com/2013/07/17/what-is-resonance-part-3/)
5 Videos That Explain Resonance (https://blog.prosig.com/2011/09/20/5-videos-that-explain-resonance/)

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#### James Wren

Former Sales & Marketing Manager at Prosig
James Wren was Sales & Marketing Manager for Prosig Ltd until 2019. James graduated from Portsmouth University in 2001, with a Masters degree in Electronic Engineering. He is a Chartered Engineer and a registered Eur Ing. He has been involved with motorsport from a very early age with a special interest in data acquisition. James is a founder member of the Dalmeny Racing team.

### This Post Has 42 Comments

1. Armani Shepherd

Dear James,
Your blog and explanations are really helpful – thanks. I’m a music student whose been asked to analyze and write about the Islamic call to prayer. During my research it became evident that in some countries the muezzin (caller) is being replaced by a pre-recorded version of the prayer (adhan). Hypothetically speaking, based upon the ‘sympatethic resonance’ effect might it be catistrophic if all 3,000 mosques in a a city (i.e. Istanbul) played the same adhan five times daily. If the sound was played collectively over loudspeakers could this produce a ‘walls of Jericho’ effect. Presently there is a ‘desynchronization’ of sound as various muezzin-s start calling at slightly different times, with different maqams (scales) and melodies, however I was just wondering…. Could a single call to prayer broadcasted across a city be problematic or when mosques and buildings are designed they automatically are damped so it won’t matter?

I’m a far better musician than I ever have been at physics or chemistry hence my question here…. your reply woud be most helpful.

Regards
Armani

2. Hello Armani,

Thank you for asking a question on our blog.

Your question is very interesting, it is however not possible for any damage to occur to a building structure from the co-ordinated playing of music.

From a structural point of view the buildings would not be affected for two reasons, the first reason is the frequency of the music is far too high to have any effect on structures of that sort. The sound waves would simply pass straight through.
Second, the magnitude of the sound wave would need to be very large to actually have enough power to excite a large structure.
With regards to constructive sound, this would happen if two points, or sound sources, had exactly the same music, and played it at exactly the same time. Exactly in between the two sound sources as the sound waves passed through each other there would be a constructive effect.
This is at that exact point the music would be louder.

3. Further to James’ comments I would add that structural damage is only likely to happen when there is high amplitude,low frequency excitation present(either impulsive or periodic. The “walls of Jericho” phenomenum is more likely to have been caused by the seismic impulses of the army marching in step around the city rather than due to the sound of the trumpets. The main contribution of the brass instruments was probably to improve the synchronisation of the marching soldiers.

4. Armani Shepherd

Thank you very much. You have both been most helpful. Thanks.

5. F.Benjamin Franklin

HI,
I conducted a vibration test in a shaker machine. I applied 1 g acceleration and monitored the acceleration of the test piece. A linear sweep wave ranging from 30 Hz to 3500 Hz at 300 sec. The output acceleration curve shows some narrow peak points ( first one is acceleration peaked to 6g in a frequency range of 1110 Hz to 1130 Hz Hz. Second one is 5.16 g in a frequency range of 1325 Hz to 1500 Hz . Third one is 4.6 g in a frequency range of 1500 Hz 1650 Hz). But no significant increase in noise level is observed during this time. But a smoother increment in acceleration curve I observed was for 17 g in a frequency range of 2975Hz to 3495 Hz. Here there was a significant increase in noise level. I conducted a FEA for the same and found first natural frequency at 2900 Hz. My questions are, 1)What is the importance of noise curve? 2) How to interpret the narrow peaks? 3) Whether the first natural frequency is between 2975 to 3495 or prior to this peak like 1120 Hz? Kindly explain.

Benjamin Franklin,
Chennai, India.

6. Hello Benjamin,

Thanks for asking a question on our blog.

It sounds like the peaks your seeing are the natural frequencies of the structure your exciting.

Your Finite Element Analysis is giving you a natural frequency of 2700Hz, from the practical testing you have carried out it would appear to be inclusive. You say you have performed the test twice, but you have quite different results each time. Any practical test should be repeatable, no matter how many times you carry out the same test you should get the same results. I would suggest carrying out the practical tests again, perhaps repeating the test three times to make sure no experimental error is creeping into the testing.

Please feel free to come back and let us know your new results.

7. Benjamin Franklin

Dear James,
Thanks for your reply. I did not mention that I conducted the test twice. I intended to tell that those are the narrow peak curves I got when I swept the frequency from 30 Hz to 3500 Hz. Kindly draw a curve between Frequency and acceleration based on my values. Let the acceleration values for frequencies I did not mention be 1 g.I would like to ask you the significance of noise curve. Whether the narrow peaks makes sense even though there is no sign of noise level. Hope you understand my question. Kindly explain.

8. Hello Benjamin,

Thank you for asking another question on our blog.

I don’t think we can give you advise on your project exactly, we do not know what your structure is for example. Generally I would not expect to see very small spikes, that would mean there is very little energy in those bands and that the structure was only being excited in a very small band, which is not impossible, but unlikely. I would suggest looking again at your test procedure and the signal processing techniques you are using.

If you would like to discuss this further perhaps it would be best to contact us directly.

9. Ricer

Hi James,I found your blog very helpful. I got a question to ask you. At one time of our testing, a resonant vibration at 2072 Hz and 34.26g in a valve had been found by some vibration measurements. We then measured in a separate test the natural frequency of one moving part by exciting the part by a special hammer which comes with a vibration measurement instrument. Its natural frequency is about 2000 Hz. I would like to know how I can find out the exiting frequency that caused the resonant vibration at 2072 Hz in our valve testing. Appreciate your help.

10. Hello Ricer,

Thanks for posting on our blog.

From what you have said you have a system which when tested had a resonant frequency of 2072Hz.

You then performed a separate test on a part of the system and found it had a resonant frequency of approximately 2000Hz.

And your question is that you are trying to find what had excited the system in the first place that then caused the resonance.

This is classical testing and analysis problem. I don’t know what your system is so I can’t offer you any specific advice, but generally if you have several inputs to a system you can simply remove them one at a time until you find the cause. There are more complex techniques but we would have to know more about your system to cover the more complex issues. You could for example consider something like Source Contribution Analysis, this could rank the inputs and show you which frequencies are being excited by which input.

If you would like to discuss this further perhaps it would be best to contact us directly.

11. Ricer

Hi James, Thanks for the quick response. Let me simplify it to a more general question- if one has a vibration source in the system, say, 100 Hz. It can cause the resonances of 100, 200, 300 Hz,…. Is this correct? If there is a resonant frequency in the system in line with one of these frequencies, a resonant vibration would occur. Is this correct? As I observed a resonant vibration at 2072 HZ, could I say that what had excited the system had a frequency of 2072/n Hz (n is an integer)? Is it correct? Thanks again for your time. Appreciated your help.

12. Hello Ricer,

You have tested the system separately and found its resonance frequency to be 2072Hz, these results you deduced from hammer impact testing.

If the system had a resonance at 100Hz this would be excited by your 100Hz input. But if your system had a 200Hz resonance this would also be excited by your input of100Hz as one of the harmonics would fall at 200Hz and so on.

I hope this is clear for you and this information helps.

13. vishwas

Sir,i wanted to know why we are going to find the fundamental natural frequency? (first mode of vibration) and which mode shape/ which frequency should be considered as natural frequency of a structure when there are infinite natural frequencies.

14. vishwas

sir we can find the natural frequencies of a structure in any software ( STAAD or Nastran-patran)how about the excitation in these cases? without any external excitation how can we get natural frequencies?

15. Hello Vishwas,

Thanks for asking some questions on our blog.

It is possible make a judgement on a natural frequency without excitation, but you have to consider many other issues.

Your better to isolate a structure and test it in isolation with measured excitation. That is the best way to find the natural frequencies.

16. Belinda Jiang

Dear Ricer,
Very glad to find your blog here. And now i am finding some materials about “resonance point vibration durability test”. I think your blogs may not focus on reliability test, as a quality engineer, i want to learn the result of this resonnance point, how about its effect to our product after long time working.
And the most difficult question for me to define is the resonance point vibration test cycle and its duration time. How to calculate?
Looking forward to your reply, as i am not a English-speaking people, hoping you can understand my question.
Thank you!

17. Hello Belinda,

Thank you for asking a question on our blog.

For sure resonance will affect the long term reliability of your products.

Generally speaking products are designed so that in normal use the resonant frequency is never excited.

If your product is used at a range of frequencies that include its resonant frequency your testing should replicate the range of frequencies that the product will be exposed to during its working life. If you are trying to accelerate the life testing of a product then you can subject the product to higher levels of the same frequency that it would otherwise be exposed to. The increase in level is proportional to the acceleration and therefore life testing of the product.

18. Belinda Jiang

Dear James,

19. I found this info is very useful. Thanks for sharing. Do you mind if I mention a few lines written in this article in our website if it’s acknowledged you as the writer and links back to this site? Thank you!

20. Hello Cherri,

Please feel free to mention a few lines in the article on your web site, but please do make sure to refernce us here at Prosig and provide a link to our article or web site.

21. Lin

Hi James

I just found out this blog and find it very well explained. May I know if the resonance frequency of the structure is known, can we predict/relate how the structure will react during random vibration.

1. Hello Lin,

Thank you for asking a question on our blog.

To answer your question, the simple answer is no. If you know the resonance then you know the behaviour of your structure if it is excited at that particular frequency only. So where the structure excited with random vibration the resonance and many other frequencies may be excited. So to predict or know the response to a range of vibration frequencies, like random excitation would require testing to those frequencies.

22. V Negi

Its really informative and quite methodical.

23. Juan

Hello James,
Can you please explain natural frequency and resonance, and how they can relate.

1. Hello Juan,

Thank you for asking a question on our blog.

Basically the terms have the same meaning.

In simple terms resonance is the condition at which a system responds with a maximum amplitude to a given periodic driving force.

For example a mechanical system could potentially have a number of frequencies at which resonance can occur.

These frequencies would be called the natural frequencies.

The lowest of these natural frequencies is often called the fundamental frequency, the other frequencies are multiples of this fundamental.

When resonance occurs you could say that the driving force has the same value as one of the natural frequencies.

24. Matt

Hi James,
I am having trouble understanding what the fundamental frequency is. Is this the frequency at which a material etc will vibrate at once the material is excited. For an investigation I will be doing, I will be dropping a specific object onto a bech for example and using an accelerometer measure the vibrations in the bench. I will then put this data into a fourier transform and analyse the frequencies. Will the momentum of the object hitting the bench affect the fundamental frequency recorded? Also I am wanting to know what harmonics are.

Regards Matt

1. Hello Matt,

Thank you for asking a question on our blog.
I understand your troubles, it is a very common source of confusion.

In your example the frequencies you measure in your bench will not change with the different momentums of the object your dropping on the bench. That is true, but based on several assumptions.

I’ll try to explain, a church bell when hit with a hammer will make a certain sound. It makes this certain sound due to it’s physical size and shape, these parameters control it’s resonant frequency. No matter how hard (within reason) the bell is hit the sound is the same.

Now actually life is never that simple and their probably will be some changes to the frequency signature, but the resonant frequency should be very clear in every case, assuming you have excited the structure with the energy required to excite it’s resonance and that your excitation frequency range covers the frequency range of the resonance.

Harmonics are multiples of that resonance, so if the resonance was 100Hz you might find a peak at 200Hz which is related to the resonance by a factor of 2 for example, there could be many harmonics like this.

25. Brian

Hi James,

Thanks for your informative post. I’ve been studying noise and vibration control for almost a year and still seeking explanations and answers on how to reduce it’s noise and vibration. My idea about resonance and vibration is elaborated, thanks to your blog.

1. Hi Brian,

26. Mohammed

Hello James , Would you please be so kind as to explain and comment about the phase shift in physical way ? why there is phase shift change at the resonance ? or what is the phase shift in more clear physical way . I would very much appreciate if your answer would be with example to understand the basic principles of this . For clarity I am reading about collocated systems in which I excite them with triangle waveform and peak resonance will occur as inherent property of piezoelectric ?

1. Hello Mohammed,

Thank you for asking a question on our blog.

So your question, reformed if I may, is why is there a phase shift at resonance?

At resonance the system will no longer behave as when not at resonance.
Consider a simple spring, one end free and the other being driven by the force of piston pushing up and down up on the spring.

The spring will extend and contract in phase with the piston’s excitation force.
But at resonance that relationship changes. The spring would move in the opposite direction to the excitation force. So at the piston applies force to the spring, but the spring would get shorter!

That is what is actually happening the the system at resonance, that’s why the phase changes.

Your regards to your further question related to triangular wave forms, these are created from a number of components with various harmonics and are therefore quite broadband in nature compared to a simple sine wave for example. So a triangular wave is generally more likely to excite resonance in a system as it would exciting the system across a larger range of frequencies compared to a pure sine wave..

27. Dhruvit Modi

Hi I am working on car brake system. I found out we have resonance and annoying moan noise at 250Hz. I have few questions.

(1) Could I find out which components have 250Hz by performing free-free modal analysis of each component? or I need to perform modal analysis for each component by fixing the component the way it is mounted in vehicle?
Free-free and fixed both provide different frequency values but it is really hard to perform fix modal analysis of each component the way it is fixed in vehicle. Basically my question is how free-free and fixed component modal analysis are useful?

(2) We have narrow peaks at frequency mentioned above. I believe it means two parts are having frequency in range of 250Hz. If I find out which components are having natural frequency at 250Hz then how much frequency shift should I maintain in order to remove resonance. For example if one part has 250Hz then how much natural frequency shift should be maintained for other part to avoid resonance? Is there any common value like 10% or 15% natural frequency shift between 2 parts is require to avoid resonance?

(3) How many surrounding components should be checked to find avoid which part is contributing for resonance. I mean should I check modal for each component of car or should I make it specific to brake assembly and other assemblies which are getting connected to brake assemblies like suspension assembly. How to draw a line for finding out which component could contribute in resonance?

1. Hi Dhruvit,

Thank you for posting a question on our blog.

I understand the project your working on.

1,
Its a matter of opinion actually, I would always suggest testing free-free, but some people prefer to test in place as they say the structure stiffness or mass is changed when in place and therefore the frequencies are changed. I believe if you test each part free-free you will find the part with the resonance at the frequency of interest more clearly

2,
The answer is no, but there is no stock correct or incorrect answer, the resonance should be as far away as possible from the excitation frequency. I have seen 30% used in the past, but as I said there is no right or wrong.

3,
Good question, whole vehicle modal analysis takes teams of engineers weeks or months to perform let alone analyse, for that reason alone it is not often or lightly considered. The simple answer would be to perform some source contribution analysis to find which brake system part is the issue, then you could clearly see which parts of the suspension or similar is connected to that specific part, and thus you could follow towards performing more SCA as required.
I like SCA as it’s so quick and easy to do.

28. Mr James, thanks for your prompt and quality answers to people questions.
I wish to have your direct contact for clarification of issues regarding “RESONANCE” thanks in anticipation. E.O. Richard.

29. Donald Hartwick

James

What do you call a first resonance point

30. Donald Hartwick

sorry was not clear what do you consider a resonance two times input ?

1. Hi Donald,

Thank you for posting on our blog.

The first natural frequency is often called the resonant frequency.
Sometimes it is also called the first mode.

The second mode and third mode would therefore be multiples of the first mode.

31. Quim Cahayagan

Hi James,

I am working on steel mill plant and we encounter some problems about vibration. I used the modal analysis to calculate the frequencies and mass participation of different mode shapes. For example the machine has a frequency of 29.7 Hz, based on the results 1) how to determine the natural frequency of the structure to avoid the resonance effect? 2) Do i need to consider all natural frequencies up to 90% mass participation and check it individualy? 3) Using modal analysis what are the criteria to consider to avoid resonance effect on the structure?

Any inputs would help a lot. Thank you!

1. Hello Quim,

Thank you posting a question on our blog.

To find the natural frequency of a structure we would use Hammer Impact Analysis, Prosig have a system especially for this purpose.

In short, using a force gauge instrumented hammer, to measure the excitation force and a response accelerometer to measure the response.
The software will create an FRF that will show the natural frequencies of the structure.

Then you would check, using the accelerometer, the excitation frequencies when the machine is in use.

If, during normals use, the structure is being excited at a natural frequency, you have a problem. If not, then no problem.
When there is a problem the excitation frequency needs to change, that is change the speed of the machine, or change the design, mass or stiffness.

Reading between the lines, it looks rather like the work you have done and the further work you’re proposing is based in simulation. We would always recommend practical test over simulations. In our experience practical test and simulations tend not to come to the same conclusions.

32. Is every resonating frequency is a natural frequency of a system?

1. Hello Swapnil,

Thank you for asking a question on our blog.

I think to answer your question we have to focus on what is a natural frequency? And what is a resonance?

So what is a natural frequency?
The simple answer is the frequency at which a system oscillates when not subjected to an external force.

So then what is resonance?
In short the resonant frequency is the frequency at which a driving force of a particular frequency has the ability to produce large amplitude oscillations in the test piece.

So going back to your original question, again in simple terms, what would happen if the driving frequency and the natural frequency were the same? The answer is resonance.